Question

How can I solve these problems?

Answer 1

what is that p word ?
sequence to see what ..... generated?
...
anyways I also see it says find some terms
let's find the first 5 terms for a and see what they look like
first term is given a_1=2
to find the second term enter in 1 for n this will give you on the left hand side a_2
try it

Answer 2

pattern..

Answer 3

can u give me an example? I don't know what you are talking about. sorry

Answer 4

You don't see n?

Answer 5

\[a_1=2 \\ a_{n+1}=a_n+2 \]
You see those n's ?

Answer 6

in the subscript area?

Answer 7

replace them with 1

Answer 8

\[a_{1+1}=a_1+2 \]

Answer 9

now that first subscript can be simplified to 2 so you have
\[a_2=a_1+2\]

Answer 10

but a_1 is 2
so you know \[a_2=2+2\]

Answer 11

so a_2 is 4
that is the second term of the sequence is 4

Answer 12

try finding a_3 now

Answer 13

replace the n's with 2 instead of 1

Answer 14

ok

Answer 15

is it 10?

Answer 16

\[a_{n+1}=a_n+2 \\ \text{ replace } n \text{ with 2 } \\ a_{2+1}=a_2+2 \\ a_3=a_2+2 \\ \text{ we just found } a_2 \text{ to be 4 }\]

Answer 17

6?

Answer 18

yes 4+2 is 6

Answer 19

not 10

Answer 20

so far we have
2,4,6 are the first three terms of the sequence in order

Answer 21

you can find the 4th term if the you aren't sure what pattern is here so far

Answer 22

why did u add the 4 with 2? even though, the problem said to add with 5?

Answer 23

because it says to add 2

Answer 24

\[a_{n+1}=a_n+2 ; a_1=2 \\ \text{ replace } n \text{ with 1 } \\ a_{1+1}=a_1+2 \\ a_2=a_1+2 \\ \text{ we are given } a_1 \text{ is } 2 \\ a_2=2+2=4 \\ \text{ now replace the } n's \text{ with 2 } a_{2+1}=a_2+2 \\a_3=a_2+2=4+2=6\]

Answer 25

I thought u were doing problem b. nevermine

Answer 26

thanks

Answer 27

oh no I have been working with a from the very go

Answer 28

okay, yea that's why I was confused.

Answer 29

that is why i kept adding 2 and not 5

Answer 30

yea, I understand now

Answer 31

Can you help with question 5 also?

Answer 32

have you done number 4 yet
I think that might be important for 5
because I think the difference equations they are talking about are the one's in 4
could be wrong about that

Answer 33

you can find the first few terms and should be able to match it to a sequence in 4

Answer 34

still doing number 4

Answer 35

for example 4a is 2,4,6,8,10,... and so on...
5d is also 2,4,6,8.10,...
I know this from finding the first few terms
\[a_n=2n \\ a_1=2(1)=2 \\ a_2=2(2)=4 \\ a_3=2(3)=6 \\ a_4=2(4)=8\]
and so on...

Answer 36

we clearly see that 5d is equivalent to 4a

Answer 37

ahh i think i will have to match the equations from question 4 to the equations in question 5 right?

Answer 38

that is what I'm thinking

Answer 39

I am having a problem with question 4, e. Can you explain how to do that to me.

Answer 40

you could do 4d though ?

Answer 41

e and d are very similar

Answer 42

mhm I guess I don't know how to do d either then. I thought it was just adding 1 everytimes for the d.

Answer 43

oh no

Answer 44

let's look at 4d then

Answer 45

\[a_{n+1}=-a_n ; a_0 =1 \]
this is what is given

Answer 46

so they are using a_0 as first term instead of a_1

Answer 47

so we need to find the second term a_1
to do this we need to replace n with 0

Answer 48

\[a_{0+1}=-a_{0} \\ a_1=-a_0\]

Answer 49

we are given a_0 is 1 right

Answer 50

we are given a_0 is 1 right\[a_1=-(1) \\ a_1=-1 \]

Answer 51

it is multiplication not addition

Answer 52

\[a_{n+1}=-a_n \text{ can be read like this } \\ a_{n+1} =(-1)a_n\]

Answer 53

\[\text{ or like this } a_{n+1} =-1 \cdot a_n\]

Answer 54

first term is 1
second term is -1(1)=-1
third term is -1(-1)=1
we are just taking the previous term and multiplying it be -1 to get the term after

Answer 55

Okie, I did all the steps correct then, just got the pattern wrong.

Answer 56

for it would it be like this ----- a1 + 1 = 2a1 --- a2 = 4?

Answer 57

e*

Answer 58

I'm not totally sure what all that is before the a2=4 thing
but if you are saying a2 is 4 then you are right because
2(2)=4

Answer 59

so just like before to get the term in question we are taking the previous term and multiplying it by 2 (instead of -1)

Answer 60

yea that's what I did :D. Thank you so much. U helped me alot!

Answer 61

cool stuff
it should be kinda obvious which choice from 4 should match up with what choice from 5
since I told you 4a=5d
I say this because 4b and 4c are similar to 4a

Answer 62

so do you think you can match them all up even without finding the first few terms?

Answer 63

yes, i finished it already

Answer 64

nice work

Answer 65

thanks. u too